Solid spherical particles having a diameter of 0.080 mm and a solid density of 2600 kg/m³ are settling in a solution of water at 26.7°C. The volume fraction of the solids in the water is 0.45. The density of water is 997.7 kg/m³ and the viscosity of water is 0.861 x 103 Pa•s. Calculate the settling velocity and the Reynolds number.

3 A constant-density Newtonian fluid is flowing as a thin film down a vertical wall in laminar flow; see Fig. 15.9. a. Find the velocity distribution and the volumetric flow rate per unit width of wall by using the Navier-Stokes equations (z component) on the assumptions that there is no flow in the x or y direction, that the z component of the velocity is zero at the solid wall, and that there is no shear stress at the liquid-air surface, and the flow is steady-state. (Waves may appear on the fluid surface in this situation; ignore that possibility for this problem). Solid wall * Air Thin liquid film Thickness Ax FIGURE 15.9 A thin liquid film flowing down a wall. b. Repeat the solution to Prob. 3a, showing both the velocity distribution and the volumetric flow rate, for the case in which the flow under the influence of gravity is between two parallel vertical plates, separated by the distance Ax. In Prob. 15.9 the pressure gradient in the flow direction was zero, because the film was…

17.29 An engineered tissue system consists of a slice of cell mass immobilized on a scaffold measuring 5 cm in length and 0.5 cm in thickness. The top face of the tissue scaffold is exposed to water, dissolved oxygen, and organic nutrients maintained at 30 C. The bottom face of the tissue is thermally insulated. At present, the specific oxygen consumption of the tissue mass is 0.5 mmol O₂/cm³cells-hr, and from respiration energetics, the energy released by respiration is 468 J/mmol O₂ consumed. We are interested in knowing the temperature at the bottom face of the tissue next to the insulated boundary. If this temperature remains below 37 C, the tissue will not die. The thermal conductivity of the tissue scaffold is k = 0.6 W/m. K. a. Using the information given predict the temperature profile within the tissue slab the slab. b. C. What is the heat generated per unit volume of tissue? Estimate the temperature at x =L (the insulated boundary).

Consider the problem of how plants might lift water from ground level to their leaves. Assume that there us a semipermeable membrane at the roots, with pure water on the outside, and an ideal solution inside a small cylindrical capillary inside the plant. The solute mole fraction inside the capillary is x = 0.001. The radius of the capillary is 0.1 mm. Assuming the density of the solution = 1 g/mL, what is the height of the solution at 298 K? Can osmotic pressure account for raising this water?